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Tangents and Normals (HSC SSCE Mathematics Advanced): Quizzes

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Tangents and Normals

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What is a tangent line at point $(a, f(a))$ on a curve?

A line touching the curve with same gradient

How do you find the gradient of the tangent to $y = f(x)$ at $x = a$ ?

Calculate $f'(a)$

What is the gradient of a horizontal tangent?

$0$

If the tangent has gradient $m_T$ , what is the relationship with normal gradient $m_N$ ?

$m_T \times m_N = -1$

If the tangent gradient is $f'(a) = -3$ , what is the gradient of the normal?

$\frac{1}{3}$

What is the angle of inclination of a line?

Angle with +ve x-axis anticlockwise

What is the relationship between gradient $m$ and angle of inclination $\theta$ ?

$m = \tan \theta$

If a tangent has a negative gradient, what type of angle of inclination does it have?

Obtuse ( $90° < \theta < 180°$ )

What is the equation of the tangent to $y = f(x)$ at point $(a, f(a))$ ?

$y - f(a) = f'(a)(x - a)$

If a normal has gradient $\frac{1}{3}$ , what is the gradient of the tangent?

$-3$

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Tangents and Normals (HSC SSCE Mathematics Advanced): Quizzes

Practise the questions

What is a tangent line at point (a,f(a))(a, f(a))(a,f(a)) on a curve?

How do you find the gradient of the tangent to y=f(x)y = f(x)y=f(x) at x=ax = ax=a?

What is the gradient of a horizontal tangent?

If the tangent has gradient mTm_TmT​, what is the relationship with normal gradient mNm_NmN​?

If the tangent gradient is f′(a)=−3f'(a) = -3f′(a)=−3, what is the gradient of the normal?

What is the angle of inclination of a line?

What is the relationship between gradient mmm and angle of inclination θ\thetaθ?

If a tangent has a negative gradient, what type of angle of inclination does it have?

What is the equation of the tangent to y=f(x)y = f(x)y=f(x) at point (a,f(a))(a, f(a))(a,f(a))?

If a normal has gradient 13\frac{1}{3}31​, what is the gradient of the tangent?

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Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

What is a tangent line at point $(a, f(a))$ on a curve?

How do you find the gradient of the tangent to $y = f(x)$ at $x = a$ ?

If the tangent has gradient $m_T$ , what is the relationship with normal gradient $m_N$ ?

If the tangent gradient is $f'(a) = -3$ , what is the gradient of the normal?

What is the relationship between gradient $m$ and angle of inclination $\theta$ ?

What is the equation of the tangent to $y = f(x)$ at point $(a, f(a))$ ?

If a normal has gradient $\frac{1}{3}$ , what is the gradient of the tangent?